Philosophy Of Science

Alexander Bird

• Publisher: Routledge
• Year: 2006
• ISBN:
  9781135364229
• Edition: 1
• Topic: Philosophy
• Subtopic: Philosophy History & Theory

An up-to-date, clear but rigorous introduction to the philosophy of science offering an indispensable grounding in the philosophical understanding of science and its problems. The book pays full heed to the neglected but vital conceptual issues such as the nature of scientific laws, while balancing and linking this with a full coverage of epistemological problems such as our knowledge of such laws.

Part I
Representation

Chapter 1

Laws of nature

The notion of a law of nature is fundamental to science. In one sense this is obvious, in that much of science is concerned with the discovery of laws (which are often named after their discoverers—hence Boyle’s law, Newton’s laws, Ostwald’s law, Mendel’s laws, and so on). If this were the only way in which laws are important, then their claim to be fundamental would be weak. After all, science concerns itself with much more than just the uncovering of laws. Explaining, categorizing, detecting causes, measuring, and predicting are other aims of scientific activity, each quite distinct from law-detecting. A claim of this book is that laws are important because each of these activities depends on the existence of laws. For example, take Henry Cavendish’s attempt to measure the gravitational constant G using the torsion balance. If you were to have asked him what this constant is, he would have told you that it is the ratio of the gravitational force between two objects and the product of their masses divided by the square of their separation. If you were then to ask why this ratio is constant, then the answer would be that it is a law of nature that it is so. If there were no law of gravitation, then there would be no gravitational constant; and if there were no gravitational constant there would be nothing that counts as the measurement of that constant. So the existence and nature of a law was essential to Cavendish’s measuring activities. Somewhat contentiously, I think that the notion of explanation similarly depends upon that of law, and even more contentiously I think that causes are also dependent on laws. A defence of these views must wait until the next chapter. I hope it is clear already that laws are important, a fact which can be seen by considering that if there were no laws at all the world would be an intrinsically chaotic and random place in which science would be impossible. (That is assuming that a world without laws could exist—which I am inclined to think doubtful, since to be any sort of thing is to be subject to some laws.) Therefore, in this chapter we will consider the question: What is a law of nature? Upon our answer, much that follows will depend.

Before going on to discuss what laws of nature are, we need to be clear about what laws are not. Laws need to be distinguished from statements of laws and from our theories about what laws there are. Laws are things in the world which we try to discover. In this sense they are facts or are like them. A statement of a law is a linguistic item and so need not exist, even though the corresponding law exists (for instance if there were no people to utter or write statements). Similarly, theories are human creations but laws of nature are not. The laws are there whatever we do—one of the tasks of the scientist is to speculate about them and investigate them. A scientist may come up with a theory that will be false or true depending on what the laws actually are. And, of course, there may be laws about which we know nothing. So, for instance, the law of universal gravitation was discovered by Newton. A statement of the law, contained in his theory of planetary motion, first appeared in his Principia mathematica. In the following we are interested in what laws are—that is, what sort of thing it was that Newton discovered, and not in his statement of the law or his theories containing that statement.⁸ Furthermore, we are not here asking the question: Can we know the existence of any laws? Although the question “What is an X?” is connected to the question “How do we know about Xs?”, they are still distinct questions. It seems sensible to start with the former—after all, if we have no idea what Xs are, we are unlikely to have a good answer to the question of how we know about them.

Minimalism about laws—the simple regularity theory

In the Introduction we saw that the function of (Humean) induction is to take us from observations of particular cases to generalizations. It is reasonable to think that this is how we come to know laws—if we can come to know them at all. Corresponding to a true inductive conclusion, a true generalization, will be a regularity. A regularity is just a general fact. So one inductive conclusion we might draw is that all emeralds are green, and another is that all colitis patients suffer from anaemia. If these generalizations are true, then it is a fact that each and every emerald is green and that each and every colitis sufferer is anaemic. These facts are what I have called regularities. The first view of laws I shall consider is perhaps the most natural one. It is that laws are just regularities.

This view expresses something that I shall call minimalism about laws. Minimalism takes a particular view of the relation between a law and its instances. If it is a law that bodies in free fall near the surface of the Earth accelerate towards its centre at 9.8 ms−2, then a particular apple falling to the ground and accelerating at 9.8 ms−2 is an instance of this law. The minimalist says that the law is essentially no more than the collection of all such instances. There have been, and will be, many particular instances, some observed but most not, of objects accelerating towards the centre of the Earth at this rate. The law, according to the minimalist, is simply the regular occurrence of its instances. Correspondingly, the statement of a law will be the generalization or summary of these instances.

Minimalism is an expression of empiricism, which, in broad terms, demands that our concepts be explicable in terms that relate to our experiences. Empiricist minimalism traces its ancestry at least as far back as David Hume. By defining laws in terms of regularities we are satisfying this requirement (as long as the facts making up the regularities are of the sort that can be experienced). Later we shall come across an approach to laws that is not empiricist.

The simplest version of minimalism says that laws and regularities are the same. This is called the simple regularity theory (SRT) of laws.

SRT: It is a law that Fs are Gs if and only if all Fs are Gs.

While the SRT has the merit of simplicity it suffers from the rather greater demerit that it is false. If it were true, then all and only regularities would be laws. But this is not the case.

The most obvious problem is that the existence of a simple regularity is not sufficient for there to be a corresponding law, i.e. there are simple regularities that are not laws. A criticism is also made that it is not even necessary for there to be a regularity for the corresponding law to exist. That is, there are laws without the appropriate regularities.

Regularities that are not laws

I will start with the objection that being a regularity is not sufficient for being a law. Consider the following regularities:

1. All persisting lumps of pure gold-195 have a mass less than 1,000 kg.
2. All persisting lumps of pure uranium-235 have a mass of less than 1,000 kg.⁹

Both (a) and (b) state true generalizations. But (a) is accidental and (b) is law-like. It is no law that there are no lumps of the pure isotope of gold—we could make one if we thought it worth our while. However, it is a law that there are no such lumps of uranium- 235, because 1,000 kg exceeds the critical mass of that isotope (something less than a kilogram) and so any such lump would cause its own chain reaction and self-destruct. What this shows is that there can be two very similar looking regularities, one of which is a law and the other not.

This is not an isolated example. There are an indefinite number of regularities that are not laws. Take the generalization: all planets with intelligent life forms have a single moon. For the sake of argument, let us imagine that the Earth is the only planet in the universe with intelligent life and that there could exist intelligent life on a planet with no moons or more than one. (For all I know, these propositions are quite likely to be true.) Under these circumstances, the above generalization would be true, even though there is only one instance of it. But it would not be a law; it is just a coincidence. The point here is that the SRT does not distinguish between genuine laws and mere coincidences. What we have done is to find a property to take the place of F which has just one instance and then we take any other property of that instance for G. Then “All Fs are Gs” will be true. And, with a little thought, we can find any number of such spurious coincidental regularities. For most things that there are we could list enough of their general properties to distinguish one thing from everything else. So, for instance, with a person, call her Alice, we just list her hair colour, eye colour, height, weight, age, sex, other distinguishing features, and so on in enough detail that only Alice has precisely those qualities. These qualities we bundle together as a single property F. So only Alice is F. Then choose some other property of Alice (not necessarily unique to her), say the fact that she plays the oboe. Then we will have a true generalization that all people who are F (i.e. have fair hair, green eyes, are 1.63 m tall, weigh 59.8 kg, have a retroussé nose, etc.) play the oboe. But we do not want to regard this as a law, since the detail listed under F may have nothing whatsoever to do with an interest in and talent for playing the oboe.

The minimalist who wants to defend the SRT might say that these examples look rather contrived. First, is it right to bundle a lot of properties together as one property F? Secondly, can just one instance be regarded even as a regularity? (If it is not a regularity then it will not be a counter-instance.) However, I do not think that the minimalist can make much headway with these defences.

To the general remark that the examples look rather contrived, the critic of the SRT has two responses. First, not all the cases are contrived, as we can see from the gold and uranium example. We can find others. One famous case is that of Bode’s “law” of planetary orbits. In 1772, J.E.Bode showed that the radii of known planetary orbits fit the following formula: 0.4+0.3×2ⁿ (measured in astronomical units) where n=0 for Venus, 1 for the Earth, 2 for Mars, and so on, including the minor planets. (Mercury could be included by ignoring the second term, its orbital radius being 0.4 astronomical units.) Remarkably, Bode’s law was confirmed by the later discovery of Uranus in 1781. Some commentators argued that the hypothesis was so well confirmed that it achieved the status of a law, and consequently ruled out speculation concerning the existence of a possible asteroid between the Earth and Mars. Bode’s “law” was eventually refuted by the observation of such an asteroid, and later by the discovery of the planet Neptune, which did not fit the pattern. What Bode’s non-law shows is that there can be remarkable uniformities in nature that are purely coincidental. In this case the accidental nature was shown by the existence of planets not conforming to the proposed law. But Neptune, and indeed Pluto too, might well have had orbits fitting Bode’s formula. Such a coincidence would still have been just that, a coincidence, and not sufficient to raise its status to that of a law.

Secondly, the critic may respond that the fact that we can contrive regularities is just the point. The SRT is so simple that it allows in all sorts of made-up regularities that are patently not laws. At the very least the SRT will have to be amended and sharpened up to exclude them. For instance, taking the first specific point, as I have stated it the SRT does not specify what may or may not be substituted for F and G. Certainly it is an important question whether compounds of properties are themselves also properties. In the Alice example I stuck a whole lot of properties together and called them F. But perhaps sticking properties together in this way does always yield a new property. In which case we might want to say that only uncompounded properties may be substituted for F and G in the schema for the SRT.

However, amending the SRT to exclude Fs that are compound will not help matters anyway, for two reasons. First, there is no reason why there should not be uncompounded properties with unique instances. Secondly, some laws do involve compounds—the gas laws relate the pressure of a gas to the compound of its volume and temperature. To exclude regularities with compounds of properties would be to exclude a regularity for which there is a corresponding law. To the second point, that the regularities con-structed have only one instance, one rejoinder must be this: why cannot a law have just one instance? It is conceivable that there are laws the only instance of which is the Big Bang. Indeed, a law might have no instances at all. Most of the transuranium elements do not exist in nature and must be produced artificially in laboratories or nuclear explosions. Given the difficulty and expense of producing these isotopes and because of their short half-lives it is not surprising that many tests and experiments that might have been carried out have not been. Their electrical conductivity has not been examined, nor has their chemical behaviour. There must be laws governing the chemical and physical behaviour of these elements under circumstances which have never and never will arise for them. There must be facts about whether nobelium-254, which is produced only in the laboratory, burns in oxygen and, if so, what the colour of its flame is, what its oxide is like, and so forth; these facts will be determined by laws of nature, laws which in this case have no instances.

So we do not want to exclude something from being a law just because it has few instances, even just one instance, or none at all. At the same time the possibility of instance less laws raises another problem for the SRT similar to the first. According to the SRT empty laws will be empty regularities—cases of “all Fs are Gs” where there are no Fs. There is no problem with this; it is standard practice in logic to regard all empty generalizations as trivially true.¹⁰ What is a problem is how to distinguish those empty regularities that are laws from all the other empty regularities. After all, a trivial empty regularity exhibits precisely as much regularity as an empty law.

Let us look at a different problem for the SRT. This concerns functional laws. The gas law is an example of a functional law. It says that one magnitude—the pressure of a body of gas—is a function of other magnitudes, often expressed in a formula such as:

where P is pressure, T is temperature, V is volume, and k is a constant. In regarding this as a law, we believe that T and V can take any of a continuous range of values, and that P will correspondingly take the value given by the formula. Actual gases will never take all of the infinite range of values allowed for by this formula. In this respect the formula goes beyond the regularity of what actually occurs in the history of the universe. But the SRT is committed to saying that a law is just a summary of its instances and does not seek to go beyond them. If the simple regularity theorist sticks to this commitment, the function ought to be a partial or gappy one, leaving out values that are not actually instantiated. Would such a gappy “law” really be a law? One’s intuition is that a law should cover the uninstantiated values too. If the SRT is to be modified to allow filling in of the gaps, then this needs to be justified. Furthermore, the filling in of the gaps in one way rather than another needs justification. Of course there may well be a perfectly natural and obvious way of doing this, such as fitting a simple curve to the given points. The critic of the SRT will argue that this is justified because this total (non-gappy) function is the best explanation of the instantiated values. But the simple regularity theorist cannot argue in this way, because this argument accepts that a law is something else other than the totality of its instances. As far as what actually occurs is concerned, one function which fits the points is as good as any other. From the SRT point of view, the facts cannot decide between two such possible functions. But, if the facts do not decide, we cannot make an arbitrary choice, say choosing the simplest for the sake of convenience, as this would introduce an arbitrary element into the notion of lawhood. Nor can we allow all the functions that fit the facts to be laws. The reason for this is the same as the reason why we cannot choose one arbitrarily and also the same as the reason why we cannot have all empty generalizations as laws. This reason is that we expect laws to give us determinate answers to questions of what would have happened in counterfactual situations—that is situations that did not occur, but might have.

Laws and counterfactuals

Freddie’s car is black and when he left it in the sun it got hot very quickly. The statement “Had Freddie’s car been white, it would have got hot less quickly” is an example of a counterfactual statement. It is not about what did happen, but what would have happened in a possible but not actual (a counter-to-fact) situation (i.e. Freddie’s car being white rather than black). The counter-factual in question is true. And it is true because it is a law that white things absorb heat less rapidly than black things. Laws support counterfactuals.

We saw above that every empty regularity will be true and hence will be a law, according to the SRT. This is an undesirable conclusion. Counterfactuals help us see why. Take some property with no instances, F. If we allowed all empty regularities to be laws we would have both law 1 “it is a law that Fs are Gs” and law 2 “it is a law that Fs are not-Gs”. What would have happened if a, which is not F, had been F? According to law 1, a would have been G, while law 2 says a would have been not-G. So they cannot both really be laws. Similarly, we cannot have both of two distinct functions governing the same magnitudes being laws, even if they agree in their values for actual instances and diverge only for non-actual values. For the two functional laws will contradict one another in the conclusion of the counterfactuals they support when we ask what values would P have taken had T and V taken such-and-such (non-actual) values.

Counterfactuals also underline the difference between accidental and nomic regularities. Recall the regularities concerning very large lumps of gold and uranium isotopes. There are no such lumps of either. In the case of uranium-235, there could not be such lumps, there being a law that there are no such lumps. On the other hand, there is no law concerning large lumps of gold, and so there could have been persisting 2,000 kg lumps of gold-195. In this way counterfactuals distinguish between laws and accidents.

Some philosophers think that the very fact that laws support counterfactuals is enough to show the minimalist to be wrong (and the SRT supporter in particular). The reasoning is that counter-factuals go beyond the actual instances of a law, as they tell us what would have happened in possible but non-actual circumstances. And so the minimalist must be mistaken in regarding laws merely as some sort of summary of their actual instances. This argument seems powerful, but I think it is not a good line for the anti-minimalist to pursue. The problem is that counterfactuals are not any better understood than laws, and one can argue that our understanding of counterfactuals is dependent on our notion of law or something like it, in which case corresponding to the minimalist account of laws will be a minimalist account of counterfactuals.¹¹ You can see that this response is plausible by considering that counterfactuals are read as if there is a hidden clause, for instance “Freddie’s car would have got hot less quickly had it been white and everything else and been the same as far as possible”. (Which is why one cannot reject the counterfactual by saying that had Freddie’s car been white, the Sun might not have been shining.) The clause which says that everything should be the same as far as possible requires among other things, like the weather being the same, that the laws of nature be the same. So one can say that laws support counterfactuals only because counterfactuals implicitly refer to laws. Counterfactuals therefore have nothing to tell us about the analysis of laws. Consider the fact that laws do not suppo...

Table of contents

• Cover Page
• Title Page
• Copyright Page
• Preface
• Introduction
• Part I Representation
• Part II Reason
• Glossary
• Notes
• Bibliography